Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.
Who should pay the Zakah (obligatory charity) from the orphan`s money?
His/her guardian, and if the latter fails to do so, then the orphan himself/herself is obliged to pay the Zakah once he/she reaches puberty, and is capable of handling his/her own affairs. And Allah Knows Best.
Is it permissible for the guardian, or the father of the child to hit the latter in order to teach him/her good manners?
It is permissible for the guardian to hit his/her child for teaching them good manners once they become ten years old provided that it is done mildly, harmlessly and without intimidation. Actually, such punishment is to be employed gradually i.e. after: asking, warning, and scolding. As for the teacher, he isn`t allowed to hit the student unless the latter`s father approves of it, and it is done according to necessity without intimidation, or harm.
Is it permissible to give the expiation due on the vow of anger to one person?
The expiation for the vow of anger-and that of the oath-is to be given to (10) needy persons, or a needy family of ten individuals, but giving it to one person is impermissible.